function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
%   parameter for logistic regression and the gradient of the cost
%   w.r.t. to the parameters.

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
%
% Note: grad should have the same dimensions as theta
%

for i=1:m,
  J += (-y(i) * log(sigmoid(X(i,:) * theta))) - (1 - y(i)) * log(1 - sigmoid(X(i,:) * theta));
end;

J = J / m;

for j=1:size(theta)(1),
  temp = 0;
  for i=1:m,
    temp += (sigmoid(X(i,:) * theta) - y(i)) * X(i,j);
  end;
  grad(j) = temp / m;
end;
% =============================================================

end
